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We study a one-dimensional Anderson model in which one site interacts with a detector monitoring the occupation of that site. We demonstrate that such an interaction, no matter how weak, leads to total delocalization of the Anderson model,…

Condensed Matter · Physics 2009-10-31 S. A. Gurvitz

We present the first rigorous result on Anderson localization for interacting systems of quantum particles subject to a deterministic (e.g., almost periodic) disordered external potential. For a particular class of deterministic, fermionic,…

Mathematical Physics · Physics 2014-02-28 Victor Chulaevsky

We establish strong dynamical localization for a class of multi-particle Anderson models in a Euclidean space with an alloy-type random potential and a sub-exponentially decaying interaction of infinite range. For the first time in the…

Mathematical Physics · Physics 2014-07-18 Victor Chulaevsky

We investigate Anderson localization of light as occurring in ultra-short excitations. A theory based on time dependent coupled-mode equations predicts universal features in the spectrum of the transmitted pulse. In particular, the process…

Optics · Physics 2010-03-15 Claudio Conti , Andrea Fratalocchi , Silvia Gentilini

We study a simple and tractable model of many-body localization. The main idea is to take a renormalization group perspective in which local entanglement is removed to reach a product state. The model is built from a random local unitary…

Disordered Systems and Neural Networks · Physics 2013-07-03 Brian Swingle

Anderson acceleration is a well-established and simple technique for speeding up fixed-point computations with countless applications. Previous studies of Anderson acceleration in optimization have only been able to provide convergence…

Optimization and Control · Mathematics 2020-06-16 Vien V. Mai , Mikael Johansson

We prove that at large disorder, Anderson localization in $\Z^d$ is stable under localized time-periodic perturbations by proving that the associated quasi-energy operator has pure point spectrum. The formulation of this problem is…

Spectral Theory · Mathematics 2007-05-23 Avy Soffer , Wei-Min Wang

For the multi-particle Anderson model with correlated random potential in the continuum, we show under fairly general assumptions on the inter-particle interaction and the random external potential, the Anderson localization which consists…

Mathematical Physics · Physics 2017-03-28 Trésor Ekanga

We develop the technique to prove localization through the analysis of eigenfunctions in presence of both exponential frequency resonances and exponential phase barriers (anti-resonances) and use it to prove localization for the Maryland…

Spectral Theory · Mathematics 2022-05-10 Rui Han , Svetlana Jitomirskaya , Fan Yang

A new KAM-style proof of Anderson localization is obtained. A sequence of local rotations is defined, such that off-diagonal matrix elements of the Hamiltonian are driven rapidly to zero. This leads to the first proof via multi-scale…

Mathematical Physics · Physics 2016-01-11 John Z. Imbrie

In this paper, we prove Anderson localization for a hierarchical Anderson-Bernoulli model on lattice with arbitrary dimension, where the potential is characterized by a geometric hierarchical structure combined with fluctuations induced by…

Analysis of PDEs · Mathematics 2026-04-22 Shihe Liu , Yunfeng Shi , Zhifei Zhang

By the famous ADE classification rational double points are simple. Rational triple points are also simple. We conjecture that the simple normal surface singularities are exactly those rational singularities, whose resolution graph can be…

Algebraic Geometry · Mathematics 2013-03-05 Jan Stevens

We develop a theory which describes the behaviour of eigenvalues of a class of one-dimensional random non-Hermitian operators introduced recently by Hatano and Nelson. Under general assumptions on random parameters we prove that the…

Condensed Matter · Physics 2009-10-30 Ilya Ya. Goldsheid , Boris A. Khoruzhenko

We study the multi-particle Anderson model in the continuum and show that under some mild assumptions on the random external potential and the inter-particle interaction, for any finite number of particles, the multi-particle lower edges of…

Mathematical Physics · Physics 2017-02-15 Trésor Ekanga

We consider the localization properties of a lattice of coupled masses and springs with random mass and spring constant values. We establish the full phase diagrams of the system for pure mass and pure spring disorder. The phase diagrams…

Disordered Systems and Neural Networks · Physics 2012-01-05 Sebastian D. Pinski , Walter Schirmacher , Rudolf A. Roemer

Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. We find that off-diagonal one- and two-particle propagators behave as gaussian random variables w.r.t. momentum summations. With this…

Disordered Systems and Neural Networks · Physics 2008-09-16 V. Janis , J. Kolorenc

Anderson localization predicts that wave spreading in disordered lattices can come to a complete halt, providing a universal mechanism for {dynamical localization}. In the one-dimensional Hermitian Anderson model with uncorrelated diagonal…

Disordered Systems and Neural Networks · Physics 2023-04-18 Stefano Longhi

Results of large-scale numerical simulations are reported on the Anderson localization in a two-dimensional square lattice tight-binding model with random flux. Localization lengths, fluctuations of the conductance, and the density of…

Mesoscale and Nanoscale Physics · Physics 2009-01-23 A. Furusaki

We use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Anderson-type models with singular distributions; in particular the case of a Bernoulli distribution is covered. The…

Mathematical Physics · Physics 2014-12-30 David Damanik , Robert Sims , Günter Stolz

As part of condensed-matter physics, the field of Anderson localization concerns the study of conductance of electrons in a random medium. We summarize and explain the results obtained in "A new numerical approach to Anderson…

Mathematical Physics · Physics 2012-07-17 Constanze Liaw